Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 10 - Parametric Equations and Polar Coordinates - Review - Exercises - Page 711: 43

Answer

The curve bulges to the right for $c \lt -1$. The curve represents a straight line for $c=-1$. The curve bulges to the left for $-1\lt c \lt 0$. We can observe a cusp for $c=0$. The curve is a loop fo $c \gt 0$. All curves have the vertical asympototes $x=1$.

Work Step by Step

The noteworthy points about the curves are the following: The curve bulges to the right for $c \lt -1$. The curve represents a straight line for $c=-1$. The curve bulges to the left for $-1\lt c \lt 0$. We can observe a cusp for $c=0$. The curve is a loop fo $c \gt 0$. All curves have the vertical asympototes $x=1$.
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